RADICALS
1. Review all definitions in Radicals, also the methods of transforming and simplifying radicals. When is a radical in its simplest form?
2. Simplify (to simplest form):
3. Reduce to entire surds:
4. Reduce to radicals of lower order (or simplify indices):
5. Reduce to radicals of the same degree (order, or index):
and
and
and
and
and
6. Which is greater,
or
?
or
?
7. Which is greatest,
or
? Give work and arrange in descending order of magnitude.
Collect:
8.
9.
10.
11. A and B each shoot thirty arrows at a target. B makes twice as many hits as A, and A makes three times as many misses as B. Find the number of hits and misses of each. (Univ. of Cal.)
Reference: The chapter on Radicals in any algebra (first part of the chapter).
The most important principle in Radicals is the following:
Hence
Or,
From this also
Multiply:
1.
by
2.
by
3.
by
4.
by
5.
by
6.
by
Divide:
7.
by
8.
by
9.
by
10.
by
11.
by
(Short division.)
12.
by
Rationalize the denominator:
13.
14.
15.
Review the method of finding the square root of a binomial surd. (By inspection preferably.) Then find square root of:
16.
17.
18.
Reference: The chapter on Radicals in any algebra, beginning at Addition and Subtraction of Radicals.